A Novel Approach for Numerical Computation of Fokker-Planck Equation

Abstract

This paper present an implementation of "modified cubic B-spline differential quadrature method (MCB-DQM)" proposed by Arora & Singh (Applied Mathematics and Computation Vol. 224(1) (2013) 161-177) for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations (ODEs), in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.